The "209" is the standard shotshell primer. Pretty much available anywhere, but prices can vary widely depending on where you are.
Getting the proper little, tiny lead balls (unless, of course, they're actually a standard size of lead shot) would likely be more difficult.
IIRC, there used to be another Italian-made replica "parlor pistol" offered by Cabela's and some othe outlets which (I think) used standard percussion caps to launch its tiny lead balls. Fashioned after a short-lived Remington "Ryder's Patent" model from the mid-to-late 18th century, I believe.
Also IIRC, at one time there were replicas of some "Flobert" type parlor guns being made but it's been too long ago for me to remember where they were made or by whom.
P.S.: I recall reading one of the "Sherlock Holmes" stories where Dr.Watson finds a bored Holmes finishing the creation of a "VR" (might've been during her Jubilee year) on a wall of their flat with a parlor pistol of some sort, most likely one which used the so-called "Flobert cap" ammo.